Equivalent mechanical models

Abstract

Introduction Generally, the liquid hydrodynamic pressure in rigid containers has two distinct components. One component is directly proportional to the acceleration of the tank and is caused by part of the fluid moving in unison with the tank. The second, known as “convective” pressure, experiences sloshing at the free surface. A realistic representation of the liquid dynamics inside closed containers can be approximated by an equivalent mechanical system. The equivalence is taken in the sense of equal resulting forces and moments acting on the tank wall. By properly accounting for the equivalent mechanical system representation of sloshing, the problem of overall dynamic system behavior can be formulated more simply. For linear planar liquid motion, one can develop equivalent mechanical models in the form of a series of mass-spring dashpot systems or a set of simple pendulums. For nonlinear sloshing phenomena, other equivalent models such as spherical or compound pendulum may be developed to emulate rotational and chaotic sloshing. Graham (1951) developed an equivalent pendulum to represent the free-surface oscillations of a liquid in a stationary tank. Graham and Rodriguez (1952) introduced another model consisting of a sloshing point mass attached with springs to the tank wall at a specified depth and a fixed rigid mass. Pinson (1964) determined spring constants for liquid propellant in ellipsoidal tanks. Models in the form of mass-spring dashpot systems or a set of simple pendulums were considered by Ewart (1956), Bauer (1960a, 1961c, 1962b), Armstrong and Kachigan (1961), Abramson and Ransleben (1961c), Mooney, et al . (1964b).